2001/11/02 by Karl-Georg Schlesinger, Schlesinger, Karl-Georg · 1 citation
Mathematics · #11G55 #17B37 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:11G55 #msc:17B37
paper · pdf · doi:10.48550/arxiv.math/0111022
11 pages
arxiv created 2001/11/02 · openalex publication_date 2001/11/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce general q-deformed multiple polylogarithms which even in the dilogarithm case differ slightly from the deformation usually discussed in the literature. The merit of the deformation as suggested, here, is that q-deformed multiple polylogarithms define an algebra, then (as in the undeformed case). For the special case of q-deformed multiple zeta-values, we show that there exists even a noncommutative and noncocommutative Hopf algebra structure which is a deformation of the commutative Hopf algebra structure which one has in the classical case. Finally, we discuss the possible correspondence between q-deformed multiple polylogarithms and a noncommutative and noncocommutative self-dual Hopf algebra recently introduced by the author as a quantum analog of the Grothendieck-Teichmueller group.